The viscous surface wave problem with generalized surface energies
Analysis of PDEs
2018-06-21 v1
Abstract
We study a three-dimensional incompressible viscous fluid in a horizontally periodic domain with finite depth whose free boundary is the graph of a function. The fluid is subject to gravity and generalized forces arising from a surface energy. The surface energy incorporates both bending and surface tension effects. We prove that for initial conditions sufficiently close to equilibrium the problem is globally well-posed and solutions decay to equilibrium exponentially fast, in an appropriate norm. Our proof is centered around a nonlinear energy method that is coupled to careful estimates of the fully nonlinear surface energy.
Cite
@article{arxiv.1806.07660,
title = {The viscous surface wave problem with generalized surface energies},
author = {Antoine Remond-Tiedrez and Ian Tice},
journal= {arXiv preprint arXiv:1806.07660},
year = {2018}
}